Would single payer cover prescriptions though? Canada has single payer, and you still have to pay something whenever you get a prescription at the pharmacy.
It could. In France (which has a mixed system), single payer cover around 70% of prescriptions costs. And you usually have an additional private plan that will cover the rest (and if you're too poor to buy one of these plans, you can be eligible to get it from the state).
The NHS covers almost all drug costs. In Sweden drugs are free for kids under 18, and others have a yearly cap at ~$200 for drugs, at which they become free (partially subsidized a bit before that).
In Austria prescriptions are coveres but you pay a flat fee if the price of the prescription is higher than that flat fee.